docs: def Ergun(dp, voidage, vs, rho, mu, L=1):
      r'''Calculates pressure drop across a packed bed of spheres using a
      correlation developed in [1]_, as shown in [2]_ and [3]_. Eighteenth most
      accurate correlation overall in the review of [2]_.
  
      Most often presented in the following form:
  
      .. math::
          \Delta P = \frac{150\mu (1-\epsilon)^2 v_s L}{\epsilon^3 d_p^2}
          + \frac{1.75 (1-\epsilon) \rho v_s^2 L}{\epsilon^3 d_p}
  
      It is also often presented with a term for sphericity, which is multiplied
      by particle diameter everywhere in the equation. However, this is highly
      empirical and better correlations for beds of differently-shaped particles
      exist. To use sphericity in this model, multiple the input particle
      diameter by the spericity separately.
  
      In the review of [2]_, it is expressed in terms of a parameter `fp`, shown
      below. This is a convenient means of expressing all forms of pressure drop
      in packed beds correlations in a way that allows for easy comparison.
  
      .. math::
          f_p = \left(150 + 1.75\left(\frac{Re}{1-\epsilon}\right)\right)
          \frac{(1-\epsilon)^2}{\epsilon^3 Re}
  
      .. math::
          f_p = \frac{\Delta P d_p}{\rho v_s^2 L}
  
      .. math::
          Re = \frac{\rho v_s  d_p}{\mu}
  
      Parameters
      ----------
      dp : float
          Particle diameter of spheres [m]
      voidage : float
          Void fraction of bed packing [-]
      vs : float
          Superficial velocity of the fluid (volumetric flow rate/cross-sectional 
          area)[m/s]
      rho : float
          Density of the fluid [kg/m^3]
      mu : float
          Viscosity of the fluid, [Pa*s]
      L : float, optional
          Length the fluid flows in the packed bed [m]
  
      Returns
      -------
      dP : float
          Pressure drop across the bed [Pa]
  
      Notes
      -----
      The first term in this equation represents laminar loses, and the second,
      turbulent loses. Developed with data from spheres, sand, and pulverized
      coke. Fluids tested were carbon dioxide, nitrogen, methane, and hydrogen.
  
      Validity range shown in [3]_ is :math:`1 < Re_{Erg} < 2300`.
      Over predicts pressure drop for :math:`Re_{Erg} > 700`.
  
      Examples
      --------
      >>> Ergun(dp=8E-4, voidage=0.4, vs=1E-3, rho=1E3, mu=1E-3)
      1338.8671874999995
  
      References
      ----------
      .. [1] Ergun, S. (1952) "Fluid flow through packed columns",
         Chem. Eng. Prog., 48, 89-94.
      .. [2] Erdim, Esra, Ömer Akgiray, and İbrahim Demir. "A Revisit of Pressure
         Drop-Flow Rate Correlations for Packed Beds of Spheres." Powder
         Technology 283 (October 2015): 488-504. doi:10.1016/j.powtec.2015.06.017.
      .. [3] Jones, D. P., and H. Krier. "Gas Flow Resistance Measurements
         Through Packed Beds at High Reynolds Numbers." Journal of Fluids
         Engineering 105, no. 2 (June 1, 1983): 168-172. doi:10.1115/1.3240959.
      '''
      Re = dp*rho*vs/mu
      fp = (150 + 1.75*(Re/(1-voidage)))*(1-voidage)**2/(voidage**3*Re)
      return fp*rho*vs**2*L/dp